Quality factors for appraising resistivity LWD inversion performance

Abstract

Methods, systems, and computer program products appraise the quality of resistivity LWD data inversion and related earth models. The appraisal uses several quality factors, including signal-to-noise ratio, noise-to-signal ratio, data importance, model parameter importance, and model parameter confidence interval for the resistivity LWD data inversion and related earth models. These quality factors allow a user to determine which data provides useful information, which parts of the earth model may be relied upon, and conversely which parameters in which parts of the model may need to be modified. Such an arrangement is particularly useful in distance-to-bed-boundary (DTBB) inversion for geo-steering and formation evaluation.

What is claimed is: 
     
       1. A system for appraising resistivity inversion performance in geo-steering, comprising:
 a logging tool; 
 at least one sensor mounted on the logging tool and configured to measure signals along a portion of a well path, the signals representing one or more formation properties, including formation resistivity; 
 a formation evaluation system coupled to acquire data from a plurality of data channels representing the signals, the formation evaluation system configured to perform an inversion process using the data and a model that is derived from the data; 
 an inversion appraisal application residing in the formation evaluation system, the inversion appraisal application operable to perform an eigenvalue decomposition on the data and the model, use a result of the eigenvalue decomposition to perform an analysis of the inversion process, and provide at least one inversion quality indicator for the inversion process based on the analysis; 
 wherein the formation evaluation system is further configured to automatically select which data channels from a plurality of data channels to be used for subsequent inversions in response to the at least one inversion quality indicator exceeding an inversion quality threshold, acquire data from the selected data channels, receive an input from a user selecting certain data from the acquired data to use in subsequent inversions, and update the model using the data selected by the user to derive a final model; and 
 wherein the formation evaluation system is operable to apply the final model to determine an optimal drilling parameter for the geo-steering. 
 
     
     
       2. The system of  claim 1 , wherein the at least one inversion quality indicator includes a signal-to-noise ratio, said signal-to-noise representing a weighted or unweighted ratio of variations in data predicted by the model to variations in misfit for the inversion process. 
     
     
       3. The system of  claim 1 , wherein the at least one inversion quality indicator includes data importance, said data importance representing damped or undamped norms of data eigenvectors for the inversion process. 
     
     
       4. The system of  claim 1 , wherein the at least one inversion quality indicator includes model parameter importance, said model parameter importance representing damped or undamped norms of model eigenvectors for the inversion process. 
     
     
       5. The system of  claim 1 , wherein the at least one inversion quality indicator includes model parameter confidence interval, said model parameter confidence interval representing damped or undamped norms of ratios of model eigenvectors to model eigenvalues associated with parameters of the model for the inversion process. 
     
     
       6. The system of  claim 1 , wherein the inversion appraisal application is further operable to display the at least one inversion quality indicator as traces above the model or in a pop-up window over the model. 
     
     
       7. The system of  claim 6 , wherein the pop-up window is a visualization of Jacobian matrix elements, each matrix elements indicating a quality level for the at least one inversion quality indicator. 
     
     
       8. The system of  claim 1 , wherein the inversion appraisal application is further operable to automatically adjust the inversion process based on the at least one inversion quality indicator. 
     
     
       9. A method of appraising resistivity inversion performance in geo-steering, comprising:
 acquiring data from a plurality of data channels representing formation resistivity along a portion of a well path; 
 performing an inversion process using the data and a model that is derived from the data; 
 performing an eigenvalue decomposition on the data and the model; 
 performing an analysis of the inversion process using a result of the eigenvalue decomposition; 
 providing at least one inversion quality indicator for the inversion process based on the analysis; 
 automatically selecting which data channels from the plurality of data channels to be used for subsequent inversions in response to the at least one inversion quality indicator exceeding an inversion quality threshold; 
 acquiring data from the selected data channels; 
 receiving an input from a user selecting certain data from the acquired data to use in subsequent inversions; 
 updating the model using the data selected by the user to derive a final model; and 
 applying the final model to determine an optimal drilling parameter for the geo-steering. 
 
     
     
       10. The method of  claim 9 , wherein the at least one inversion quality indicator includes a signal-to-noise ratio, said signal-to-noise representing a weighted or unweighted ratio of variations in data predicted by the model to variations in misfit for the inversion process. 
     
     
       11. The method of  claim 9 , wherein the at least one inversion quality indicator includes data importance, said data importance representing damped or undamped norms of data eigenvectors for the inversion process. 
     
     
       12. The method of  claim 9 , wherein the at least one inversion quality indicator includes model parameter importance, said model parameter importance representing damped or undamped norms of model eigenvectors for the inversion process. 
     
     
       13. The method of  claim 9 , wherein the at least one inversion quality indicator includes model parameter confidence interval, said model parameter confidence interval representing damped or undamped norms of ratios of model eigenvectors to model eigenvalues associated with parameters of the model for the inversion process. 
     
     
       14. The method of  claim 9 , further comprising displaying the at least one inversion quality indicator as traces above the model or in a pop-up window over the model. 
     
     
       15. The method of  claim 14 , wherein the pop-up window is in the form of a matrix containing a plurality of cells, each cell indicating a quality level for the at least one inversion quality indicator. 
     
     
       16. The method of  claim 9 , further comprising automatically adjusting the inversion process based on the at least one inversion quality indicator. 
     
     
       17. A computer-readable medium storing computer-readable instructions for appraising resistivity inversion performance in geo-steering, the computer-readable instructions causing a computing system to:
 acquire data from a plurality of data channels representing formation resistivity along a portion of a well path; 
 perform an inversion process using the data and a model that is derived from the data; 
 perform an eigenvalue decomposition on the data and the model; 
 perform an analysis of the inversion process using a result of the eigenvalue decomposition; 
 provide at least one inversion quality indicator for the inversion process based on the analysis; 
 automatically select which data channels from the plurality of data channels to be used for subsequent inversions in response to the at least one inversion quality indicator exceeding an inversion quality threshold; and 
 acquire data from the selected data channels; 
 receive an input from a user selecting certain data from the acquired data to use in subsequent inversions; 
 update the model using the data selected by the user to derive a final model; and 
 applying the final model to determine an optimal drilling parameter for the geo-steering. 
 
     
     
       18. The computer-readable medium of  claim 17 , wherein the at least one inversion quality indicator includes signal-to-noise ratio, noise-to-signal ratio, data importance, model parameter importance, and model parameter confidence interval for the inversion process. 
     
     
       19. The computer-readable medium of  claim 17 , further comprising computer-readable instructions for causing the computing system to display the at least one inversion quality indicator as traces above the model or in a pop-up window over a model, wherein the pop-up window is in the form of a matrix containing a plurality of cells, each cell indicating a quality level for the at least one inversion quality indicator. 
     
     
       20. The computer-readable medium of  claim 17 , further comprising computer readable instructions for causing the computing system to automatically adjust the inversion process based on the at least one inversion quality indicator.